An efficient algorithm to locate all the load flow solutions

A novel, numerically efficient algorithm to find all the solutions to load flow equations is presented. This algorithm is based on the analysis of the topological structures of the solution set defined by the parameterized load flow equation. It is found that the load flow solutions are connected by one-dimension manifolds (curves) to form a connected graph. All the load flow solutions can be found by tracing these curves. The significance of this algorithm is that it can be guaranteed to find all the solutions while reducing the amount of computations to the point that this task can be attempted on real power systems. Results on two example systems are provided to demonstrate the numerical performance of the algorithm and to provide a comparison with the currently available method